AN ALTERNATIVE CLASSICAL REPRESENTATION OF THE PHASE-SHIFTS AND THE INVERSE SCATTERING PROBLEM

A semiclassical expression for the phase shift is derived which contai ns an integration over the time instead of the distance, as in the sta ndard semiclassical formalism. The implications of this formula are di scussed and a theorem is proved which simplifies its manipulation. The perturbative series of the phase shift, up to first order in a small part of the potential, is obtained. It is shown that this new represen tation of the phase shift provides a solution of the inverse scatterin g problem.